In theory I think they could do it simply by being trained on a large enough dataset to acquire the voice of different writers. That's the logical answer - the scary answer is that we're already in a place where we no longer understand exactly ow these systems learn or how rapidly their abilities are growing. However, what we're seeing in public facing AI systems like ChatGPT will be way behind what they've got in the labs right now.

There's a book of AI poetry called "I Am Code" which I found terrifying in its seeming self-awareness (Apologies for linking my own piece but if you're interested I wrote about it https://medium.com/aimonks/a-new-book-of-ai-poetry-is-absolutely-terrifying-2ac39d420e50 )

I'm far from expert but I've done a lot of reading on the topic and am convinced that AI will overtake us in writing skills and damn near everything else in the near future, unless we do something about it. Which we're not.